Leverkusen's superiority was fully on display.
"Disappointed that we did not go through but not frustrated or angry. Now we can focus on the league and that's what we will do," Klopp told reporters.
Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Atalanta have a chance to make history on Thursday as they welcome Liverpool to Bergamo with one foot in the Europa League semi-finals thanks to a stunning first-leg win at Anfield.
Jurgen Klopp was headed for a glorious send-off in his final season at Liverpool just a few weeks ago, but talk of a potential quadruple is now long forgotten as the Reds have come off the rails.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
"Above all, we need the bring the mentality to compete in Europe. We can say that Manchester United have returned and they are playing their best football in many years. It is a good opportunity to show that Barca can also compete," said Xavi
The former Ajax coach took over at Old Trafford last summer after the team finished sixth in the Premier League, and this season they are third, with one defeat in the last 17 games across all competitions
Barcelona and Manchester United will meet in the Europa League play-offs for a place in the competition's last 16.
Kieran Tierney’s first-half goal secured a 1-0 home victory for Arsenal over FC Zurich and top spot in Europa League Group A on Thursday, but Manchester United could only finish runners-up in their pool and will go into February’s playoffs.
Granit Xhaka's second-half winner secured Arsenal a 1-0 victory over PSV Eindhoven at the Emirates Stadium and a place in the Europa League knockout phase on Thursday.
Manchester United avoided further embarrassment after their humiliating defeat to Manchester City by coming from behind to beat Cypriots Omonia Nicosia 3-2 in the Europa League on Thursday, while Premier League leaders Arsenal eased past Bodo/Glimt.
Jadon Sancho and Cristiano Ronaldo gave timely reminders of their value with both on target as Manchester United got their Europa League campaign back on track with a 2-0 victory at Moldovan side Sheriff Tiraspol on Thursday.
Manchester United kicked off their Europa League campaign poorly with a 1-0 home defeat by Real Sociedad as Arsenal's new signing Marquinhos scored in a 2-1 win at FC Zurich on Thursday.
Chelsea hammered their London rivals Arsenal 4-1 to win the Europa League thanks to two goals from Eden Hazard, possibly making his last appearance for the Blues, and one apiece for Olivier Giroud and Pedro.
Manchester United's Paul Pogba takes a step towards helping repay his world record transfer fee with the opening goal in their Europa League win over Ajax Amsterdam.